NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  xpeq12d Unicode version

Theorem xpeq12d 4809
Description: Equality deduction for cross product. (Contributed by NM, 8-Dec-2013.)
Hypotheses
Ref Expression
xpeq1d.1
xpeq12d.2
Assertion
Ref Expression
xpeq12d

Proof of Theorem xpeq12d
StepHypRef Expression
1 xpeq1d.1 . 2
2 xpeq12d.2 . 2
3 xpeq12 4803 . 2
41, 2, 3syl2anc 642 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wceq 1642   cxp 4770
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-opab 4623  df-xp 4784
This theorem is referenced by:  opeliunxp  4820  fmpt2x  5730
  Copyright terms: Public domain W3C validator